Predictions for the Period Dependence of the Transition Between Rocky Super-Earths and Gaseous Sub-Neptunes and Implications for $eta_{mathrm{oplus}}$

One of the most significant advances by NASAu0027s Kepler Mission was the discovery of an abundant new population of highly irradiated planets with sizes between that of the Earth and Neptune, unlike anything found in the Solar System. Subsequent analysis showed that at ~1.5 $R_{mathrm{oplus}}$ there is a transition from a population of predominantly rocky super-Earths to non-rocky sub-Neptunes, which must have substantial volatile envelopes to explain their low densities. Determining the origin of these highly irradiated rocky planets will be critical to our understanding of low-mass planet formation and the frequency of potentially habitable Earth-like planets. These short-period rocky super-Earths could simply be the stripped cores of sub-Neptunes, which have lost their envelopes due to atmospheric photo-evaporation or other processes, or they might instead be a separate population of inherently rocky planets, which never had significant envelopes. We suggest an observational path forward to distinguish between these scenarios. Using models of atmospheric photo-evaporation we show that if most bare rocky planets are the evaporated cores of sub-Neptunes then the transition radius should decrease as surveys push to longer orbital periods. On the other hand, if most rocky planets formed after their disks dissipate then these planets will have formed without initial gaseous envelopes. In this case, we use N-body simulations of planet formation to show that the transition radius should increase with orbital period. Moreover, we show that distinguishing between these two scenarios should be possible in coming years with radial velocity follow-up of planets found by TESS. Finally, we discuss the broader implications of this work for current efforts to measure $eta_{mathrm{oplus}}$, which may yield significant overestimates if most rocky planets form as evaporated cores.